The play of Marienbad was popularized by film of Alain Resnais, last year with Marienbad , in 1961.

This Board game combinative abstract, of which there exist several alternatives, is played with seeds, dominos, tokens, charts, matches,… Its origin is probably very old. It belongs to the broader family of the Jeux of Nim.

This alternative was made famous for film of Alain Resnais at the point to take the name of it. In this film, the hero gains parts on parts. He pronounces this sentence with the symbolic range: I then to lose, but I always gain…

In the version of film, there are four lines, with respectively 1,3,5,7 matches and that which takes the last match loses. With each turn, the player takes the number of matches which he wants, at least one and in the same line.

Strategy:

The method rests on the Binary system. The starting position specified by the drawing opposite, is analyzed using following calculations: 1 = 0 0 1 into binary 3 = 0 1 1 " 5 = 1 0 1 " 7 = 1 1 1 " If one carries out the sums of the figures of the binary column by column bases ten of them, one finds: S = 2 2 4 All the figures of S are even, the player who will begin the part will lose if its adversary takes the care to preserve this property of S as long as this number has at least two digits. At the end of the part, it is advisable to choose S=3 or S=1 to carry it.

The strategy if that which takes the last object gains starts with the identical one, but it is necessary to aim S=4 or S=2 to the final one.

If the various combinations of play are represented, it is seen that there exists a way (one speaks about kernel: together of nodes) of blows gaining. Thus a player who is in a gaining situation and which knows the easy way is sure to gain at the end. For example, in the nontraditional play (last match = gained) one knows that the player who starts is in the kernel (S even) and is thus sure to gain whatever the actions of the adversary (and if he knows the easy way: i.e.: if it remains in the kernel), its adversary does not have its destiny between its hands.

to see Graph theory.

Play by arrangement

Beyond appearances, and although a Jeu by arrangement is a play in which one poses parts without never withdrawing some, the Play of Marienbad belongs well to this category, except that in this precise case, one withdraws in turn parts instead of posing some. In pure logic, and it is what interests us, that returns exactly to same. Indeed, one could create an apron comprising 4 lines of 1,3,5 and 7 boxes and say that the rule consists in posing in turn as many pawns as wished in a line.

External bonds

• Play of Marienbad in line

Simple: Nim

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